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Microscale Additive Manufacturing and Modeling of Interdigitated Capacitive Touch Sensors

Md Taibur Rahman1, Arya Rahimi2, Subhanshu Gupta2*, Rahul Panat1*

1 School of Mechanical and Materials Engineering, 2 School of Electrical Engineering and Computer

Science, Washington State University, Pullman, Washington 99164, USA

*Author to whom correspondence should be addressed; Email: rahul.panat@wsu.edu, sgupta@eecs.wsu.edu

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Abstract

Touch sensors have created a paradigm shift in the human-machine interaction in modern electronic

devices. Several emerging applications require that the sensors conform to curved 3-D surfaces and provide

an improved spatial resolution through miniaturized dimensions. The proliferation of sensor applications

also requires that the environmental impact from their manufacturing be minimized. This paper

demonstrates and characterizes interdigitated capacitive touch sensors manufactured using an Aerosol Jet

based additive technique that reduces waste and minimizes the use of harmful chemicals. The sensors are

manufactured with the capacitive elements at an in-plane length scale of about 50 µm by 1.5 to 5 mm, a

thickness of 0.5 µm, and a native capacitance of a 1 to 5 pF. The sensor capacitance variation is within 8%

over multiple samples, establishing the repeatability of the Aerosol Jet method. Scanning electron

microscopy and atomic force microscopy are used to characterize the sensor electrodes. 3-D

electromagnetic simulations are carried out to predict the capacitance of the printed sensors and the electric

field distribution. The simulations show a reasonable agreement with the experimental values of the

sensors’ native capacitance (within 12.5%). The model shows the native capacitance to be relatively

insensitive to the thickness of the sensor electrodes, allowing touch sensors to be fabricated with reduced

material usage and cost. The model is further used to establish the important sensor dimensions governing

its electrical performance. Lastly, electromagnetic field distribution predicted by the model is used to

establish the physical range of the touch action to be about a millimeter out of the plane of the sensors for

the geometries considered in the current work.

Key Words: Aerosol Jet printing, Printed Electronics, 3-D Printing, Wearable Devices, Touch Sensor,

Electrostatic Field Simulations, Interdigitated Capacitor, RC Time Constant.

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1. Introduction

Wearable ‘smart’ electronic devices are projected to bring transformative changes to the global

economy over the next two decades, with an associated economic value projected to be in the trillions of

dollars by 20201,2. Touch sensors form the most important type of human-machine interaction for such

devices with important uses in defense applications, robotics3, and healthcare4. The electronic circuit

enabling the touch sensors works largely through detecting the changes in input capacitance by

incorporating the distinction between varied stimuli such as stylus, single/double/multiple touch, and touch

duration5. Although such sensors are already in use, several Internet of Things (IoT) applications have

added requirements for size and conformability of the sensors per the location of the sensor circuit. In

addition, with an increase in the number of wearable devices, the environmental impact of the

manufacturing of its constituents is expected to be significant6 and requires concerted development of green

manufacturing techniques.

To date, several attempts have been made to fabricate low-cost capacitive touch sensors (or touch

panels) for various applications. A flexible capacitive sensor with encapsulated liquids as the dielectrics

was demonstrated using a MEMS-based manufacturing method7. A capacitive touch interface for RFID

tags was demonstrated, also using a MEMS-based method8. A stretchable capacitive sensor made of thin

gold film on silicone rubber was fabricated using photolithography and characterized9. A capacitive touch

panel using metalized paper was demonstrated with an effective capacitance of about 50 pF10. A foldable

direct write paper-based capacitive touch pad was developed using inkjet printing of silver nanowires at a

feature scale of 500 µm and a capacitance range from 2-40 pF11. This work11, however, did not report the

resistivity of the sintered nanowires, a critical parameter for power consumption in IoT

devices/applications12-14.

In contrast to the conventional subtractive or semi-additive MEMS-based fabrication techniques,

additive techniques such as Aerosol Jet Method (AJM)15 are being developed to fabricate passive structures.

Such methods avoid creating material waste. The AJM also requires considerably less amounts of

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environmentally harmful chemicals compared to the MEMS-based techniques. The AJM utilizes a mist of

nanoparticle inks directed by a carrier gas to print features at a length scale of 10 µm over a flat or a curved

surface and has been used to manufacture solar cells16,17, electronic interconnects18, biosensors19, strain

sensors20,21, and 3-D antenna structures22. The maximum particle size in the inks used in the AJM is typically

<500 nm23, with the sintering of the nanoparticles achieved at a temperature significantly lower than the

bulk melting point. The conductivity obtained by such methods is about 20-50% of the bulk metal22. The

AJM has also been shown to allow a standoff height (i.e., vertical distance between the nozzle printing the

ink and the substrate) up to 5 mm, enabling electronic circuits on complex 3-D surfaces22,23.

Although several manufacturing routes have been explored for touch sensors, few if any

electromagnetic simulations have been carried out to predict their native capacitance and performance as a

function of the sensor electrode morphology, dimension, and the surrounding dielectric medium. Finally, a

complete design tool with simulations and predictive modeling integrated with manufacturing could enable

rapid prototyping and development of custom-sensors at minimal costs. In addition, the sensor

manufacturing variability and its effects on the sensor electrical characteristics have not been reported

comprehensively in the literature for additive manufacturing techniques.

The present work demonstrates and characterizes printed capacitive interdigitated touch sensors

using an Aerosol Jet micro-additive manufacturing technique with the native sensor capacitance in the range

of 1 to 5 pF. The manufacturing method is shown to allow sensor feature sizes down to tens of microns,

with a capacitance per interdigitated electrode-pair of about 100 fF. Section 2 describes the sensor operating

principle, while Section 3 provides a detailed experimental procedure of sensor fabrication by the Aerosol

Jet printing. Section 4, along with supplementary information S1-3, provides details of 3-D electrodynamic

model developed to predict the capacitance of the printed sensors. The sensor measurements are described

in Section 5, while the results are presented and discussed in Section 6.

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2. Sensor Operating Principle

The schematic of the design and the operating principle of the sensor is shown in Fig. 1. The sensor

consists of an interdigitated electrode structure forming the capacitor with the probe pads connected using

interconnects (Fig. 1-a). Figures 1-b, c show the expected field lines in the untouched state and the

schematic of an equivalent electrical circuit, respectively. The coupling between the two sides of the

capacitor is expected to occur through air as well as through the glass base. Figures 1-d, e, show the expected

field-line disruptions (in air) when touched by a thumb and the schematic of its equivalent circuit with the

added capacitance, Ctouch due to the high relative permittivity of the skin/tissue/blood (εr), respectively. Note

that a thin layer of non-conductive plastic over the sensor prevents the thumb from shorting the capacitor

and will be considered in simulations. Ctouch acts in parallel to the capacitance, C0, in the untouched state,

resulting in the total capacitance, Csensor = C0 + Ctouch. Electromagnetic simulations were developed to

determine the field lines outside the sensor plane and determine the field disruption when touched. These

simulations also enabled estimating the expected capacitances prior to fabrication.

3. Sensor Fabrication

An Aerosol Jet micro-additive manufacturing machine (AJ300, Optomec Inc, Albuquerque, NM,

USA) was used to print the electrodes directly onto the glass substrate as shown in Fig. 1 (also see Fig. S1

for a picture of the equipment). An ultrasonic atomizer was used to create the aerosol/mist. The nozzle exit

diameter during printing was 150 μm, while the atomizing flow rate and the sheath gas flow rate were

maintained at 25 sccm and 50 sccm, respectively. During printing, the standoff distance between the

substrate and the nozzle was kept at about 2.8 mm. Note that the optimized parameters such as sheath gas

pressure, atomizing pressure and exhaust pressure were suitable for the ink formulation used in the current

work but may vary for other inks depending upon their viscosity, particle size and the solvent type.

The electrodes were printed using a silver nanoparticle ink (Perfect-TPS G2, Clariant Group,

Frankfurt, Germany) with a viscosity of about 1.5 cP, a particle size of 30-50 nm and a particle loading of

40 ± 2 wt %. A transparent glass slide (Thermo Fisher Scientific, Waltham, MA, USA) was used as the

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substrate. The substrates were cleaned with DI water followed by isopropyl alcohol. The substrate surface

was then further treated with an atmospheric plasma (Atomflo™ 400, Surfx® Technologies LLC, Redondo

Beach, CA, USA) at 100 W for 5 min. Before printing the structures, ink material was placed in a tube

which was rotated continuously around its axis for 12 hours using a tube roller (Scilogex MX-T6-S, Rocky

Hill, CT, USA) at about 70 rpm to prevent nanoparticle agglomeration within the ink. The printed material

was then sintered at 200 C for 30 min in a programmable oven (Neytech Vulcan furnace, Model 3-550,

Degussa-Ney Dental Inc., Bloomfield, CT, USA) to create conductive electrodes. The electrode resistivity

was measured through a 4-Wire method and was about 6.35 x 10-8 Ω-m, or about 5X of the bulk silver and

within the range reported in literature for thermally sintered nanoparticles of silver24. Three sensors were

fabricated for each of the interdigitated region lengths of 1.5, 3, and 5 mm. For the samples with 3 mm

interdigitated region length, a sensor with smaller number of electrodes (8) was also fabricated.

4. Sensor Simulation Methodology

Consistent use of additive printing (e.g. by Aerosol Jet method) will require an accurate and well-

modeled parametric library of the different variables involved. Electromagnetic simulations can be used to

study the effect of various geometrical and material parameters on the sensor behavior to aid in its design.

The simulations can also provide a quantitative picture of the electric field for the sensor geometry to further

illustrate its behavior under different conditions. We used the Momentum ADS® and EMPro® software

(Keysight®, Santa Rosa, CA, USA) in this work to develop detailed 3D models and simulation structures

for the printed touch sensors. A 2D layout was created in Momentum ADS® and then exported to EMPro

for simulation with additional 3D components using a frequency-domain finite element method (FEM)

solver. The added 3D electromagnetic (EM) components enabled detailed study of the electric fields to

understand different aspects of manufacturability and electrical behavior of the printed sensors. Both

programs are 3-D planar electromagnetic simulators used for passive circuit analysis with partial differential

equation solvers for Maxwell's equations (with boundary conditions prescribed by the users) based on the

method of moments25,26. Each model took into consideration internal and external parasitics, surface

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roughness and variations in metal thickness, dielectric constants, and detailed design parameters. A separate

3D model was created for each electrode number and length and was characterized in detail. The simulation

details, including the dimensions, parameters, meshing techniques as well as illustrations of the sensor

action with and without the touch and field line simulations are described in supporting information S1-3.

5. Sensor Measurements

An LCR meter (E4980, Agilent Technologies, Santa Clara, CA USA) was used to measure the

capacitance of an untouched printed sensor as shown in Fig. 3. The samples were grounded to a metallic

base connected to the LCR meter to minimize ground loops and improve accuracy. Proper “open” and

“short” calibrations were done prior to taking the measurements. Calibration times were set to ‘long’ to

allow precise calibration. A test fixture for the LCR meter (Model 16047A, Agilent Technologies, , Santa

Clara, CA USA) was used to convert the 4-terminal I/O into a 2-terminal I/O. Efforts were made to calibrate

the probing wires to the measuring pads of the capacitor structure to de-embed any external parasitics.

Parasitic stray admittances and residual impedances from the interconnects and the capacitor pads to the

LCR meter were compensated using ‘OPEN’, ‘SHORT’ and ‘LOAD’ correction steps in the LCR meter.

Conventional solders have a high melting temperatures and need to use flux, which can affect the

printed pads on the sensor. In addition, a soldering gun could not be used as it was observed to easily

damage the printed structures. To circumvent these problems, we used a low melting temperature solder

alloy, 52In-48Sn (Indium Corporation of America, Clinton, NY, USA) which is used for low temperature

soldering in microelectronics27, to interface with the printed structures. Small bits of the indium-based

solder, each with a size of the order of 1 mm3, were manually placed on the measuring pad and then melted

using a temperature controlled hot air gun set to about 180 ± 10 °C. The measured solder resistivity

(𝜌𝜌solder = 8.07 × 10-7 Ω-m) was found to be an order of magnitude higher than the resistivity of the

electrodes. The higher resistivity of the solder is expected to result in a lower quality factor for the capacitor

but is not expected to affect the sensor functionality in the sub-MHz frequency range. The testing apparatus

for a representative sensor is shown in Fig. S5.

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During measurements it was found that the LCR meter did not provide correct readings when the sensor

is ‘touched’ with a dry thumb (wrapped with an insulating material) due to system auto-correction as

discussed in supporting information (see section S-4). The sensor response to the touch action was

demonstrated using a RC circuit and captured on a Tektronix TDS5104B Digital Phosphor Oscilloscope.

A 300 kHz 1Vpk-pk 50% duty cycle square-wave was applied to a series resistor connected in shunt to the

capacitive sensor under test. Three repeated measurements were carried out by the same individual for a

sensor each with the interdigitated overlap lengths of 1.5, 3, and 5 mm, using this setup. The time constant

was measured based on τ = t90%−t10%2.2

(% is based on signal rise time). The time constants for the touched

and untouched state were used to obtain the ratio of the capacitance in the touched state to that in the

untouched state. This ratio along with the untouched capacitance from the LCR meter were used to get the

sensor capacitance in the touched state.

6. Results and Discussion

6.1 Printed Electrode Morphology

Figures 4-a,b,c show optical images of the capacitive sensors fabricated over a glass substrate using

the Aerosol Jet technology with interdigitated region length of 5 mm (Fig. 4-a) and 1.5 mm (Fig. 4-b) and

a total of 40 electrodes (20 per side) per sensor. Figure 4-c shows a higher magnification image of one

representative printed sensor electrode with dimensions. Prior to printing the structure, the sensor schematic

was fed to the printer using the software AutoCAD 2015 (Autodesk Inc., San Rafael, CA, USA) with

dimensions provided by the electromagnetic simulations (discussed in the next section). In addition to

varying the electrode length, some sensors were fabricated with simple variations to the original drawing,

to assess the effect on the capacitance and sensitivity. Note that the sensor electrodes also show the

formation of a ‘bulb’ at the termination and at the overlap of the electrodes and connecting lines. The bulb

formation can be controlled by the shutter speed of the deposition head of the printer. The effect of bulb

formation on the function of the sensor is expected to be minimal as it merely adds to the thickness of the

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printed electrodes in a confined area. This assumption is supported by simulations, where the sensor

capacitance will be shown to be relatively insensitive to the electrode thickness (Section 6.3). The

interdigitated region was printed using a single layer of deposited ink with individual electrodes formed by

multiple lateral (i.e. side-by-side) passes, while the electrical connection pads were printed using at least 4

layers of printed ink to allow enough mechanical strength for solder connections to the external circuit.

Figure 5-a shows the SEM image of the printed electrode after thermal curing, along with higher

magnification inset. The images clearly show surface features at an in-plane length scale of ~1 µm. The

appearance of the printed electrode surface is highly ‘rugged’ as expected from a direct-write printing

process, in contrast to the smooth surfaces obtained by other fabrication techniques such as electroplating28.

The electrode surface profiles after sintering as measured under an Atomic Force Microscope (Dimension

Icon, Bruker Corporation, Billerica, MA, USA) are shown in Figs. 5-b, c, and d. Figure 5-b shows the

profiles for the same electrode at different locations along its length, while Figs. 5-c, d show the profile of

two additional electrodes. The average electrode thickness is about 0.5µm, with a thickness varying

between 0.2 µm and about 1.7 µm. This thickness variation is high and its effect on the sensor native

capacitance and the capacitive action are discussed later in this section. Note that the observed surface

roughness could be lowered to ± 100nm range by increasing the number of passes to about ten22. In the

current study, we kept the number of passes to one for speed of the manufacturing and to reduce the material

consumed per sensor. A measurement of 15 electrodes under an optical microscope shows a width of 44.3

µm and a variation of ± 2.58 μm, or 5.8% of the electrode width. The variation in the electrode width along

a single electrode was comparable to that observed over multiple electrodes, indicating good repeatability

of the printing process by the AJM.

6.2 Electric Field

Figures 6-a,b show the equivalent simulated E-field captured with the vertical- and horizontal-

planar sensors respectively for an interdigitated structure with a total of 19 electrodes (sensor being

symmetric about one axis parallel to the length of the electrodes). The color patterns describe the

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intensity/strength of the E-fields changing from red to purple as fields becomes weaker. The E-field patterns

show some asymmetry in the z-direction which can be attributed to the coupling through the glass substrate

on one side and air on the other. The reason for the asymmetry in the plane of the sensor is not clear at this

time but is speculated to be due to the imperfections of EM mesh generated by the software for the high

aspect ratio electrodes (Fig. S3). The simulations show that the electric field extends to about 2 mm into

the space above and below the sensor (about 1 mm above the sensor top surface and about 1 mm below the

sensor bottom surface) allowing the touch action to be effective even if an external object with a different

dielectric is not touching the sensors but is present within the field. This characteristic can also be useful

for proximity sensing29 applications. Note that Fig. 6-a also shows that the field is negligible in the plane

of the sensor but outside the sensor area, suggesting that the probe pads and the interconnect lines joining

the pad with the electrodes do not significantly contribute to the system capacitance. It is interesting to note

that the classical solution of a pair of parallel plate capacitors shows that the electric field is confined within

the parallel plates30. The results for the interdigitated/comb geometry in the current study (Fig. 6-a), show

that the electric field is confined within the plane of sensor. The out-of-plane electric field, however, is not

confined by any physical features of the sensor (Fig. 6-b) and is expected to be a function of the electrode

width and gap.

6.3 Capacitance Measurements and Simulations

For the sensor in the touched state, the equivalent electrical schematic and the response of the RC

circuit (for both untouched and touched cases) captured from the oscilloscope for capacitors with 1.5 mm,

3 mm, and 5 mm interdigitated region length is shown in Figs. 7-a, b, c, and d, respectively. A delay in the

rise time for the touched state can be compared to that in the untouched state to get the ratio of the

capacitance in the respective states. The ring-up and ring-down time constants for the RC circuit response

in Figs. 7-b,c,d, are given in Table S2. The ratios of the touched to the untouched time constant for the rise

and the fall cycles are within 9% and this difference was attributed to the parasitics in the oscilloscope

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connectors which could not be calibrated out during time constant measurements. Note that the capacitance

value in the touched state was measured using the LCR meter as described in Section 5.

The sensor capacitance in the untouched state as a function of the interdigitated region length as

measured from the LCR meter (with each sensor having a total of 40 electrodes or 20 electrode pairs) is

shown in Fig. 8-a. Each data point represents an average and standard deviation of three samples. The

measured untouched capacitance showed a very low standard deviation (maximum ± 8% of the mean)

indicating good reproducibility of the AJM. The capacitance linearly increased with the interdigitated

region length. In order to get the effect of the number of electrode pairs on the capacitance, an additional

sample of 3 mm interdigitated region length was fabricated with 8 electrode pairs. The measured

capacitance as a function of electrode pairs is shown in Fig. 8-b. The simulated capacitance using

Momentum ADS® are also shown in Fig. 8-a, b and confirm the linear increase in the sensor capacitance

with length of the interdigitated region. Further, the simulations also predict that the sensor capacitance

linearly increases with the numbers of interdigitated electrode pairs. In Fig. 8-a, the difference between the

simulated values and the measured values of the capacitor is the lowest for the smallest capacitor, and

increases with the capacitor length to ± 12.5%, a reasonable agreement. The increase in the deviation

between the modeling results and the experimental measurement with the interdigitated region length is not

entirely clear but thought to be due to the relatively higher parasitics for the longer capacitor. The agreement

of the simulated capacitance of the sensor with the experimental values shown in Figs. 8-a, b is remarkable

given the actual thickness variation of the electrodes (e.g. Figs. 5-b, c, d). An explanation of this observation

is based upon further modeling results as discussed later in this section. The data used to plot Figs. 8-a, b is

given in Table S3.

Figure 8-a also shows the effect of dry thumb touch on the interdigitated capacitor, covered with a

sheet of polystyrene. The touched capacitance shows a ~2X increase over the untouched state. The standard

deviation in the measured capacitance in the touched state comes from three repeated measurements by the

same individual. Simulated values of the thumb touch (assuming εr = 40) capture the trend observed in

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experiments. The difference between the measured and simulated values is higher in the touched state, with

the difference increasing with the length of the interdigitated region of the capacitor. Note that the R-C

measurement technique does not account for any parasitic resistance or capacitance due to the external leads

connected to the equipment and is also affected by the angle of thumb placement, surface area of the thumb,

tissue thickness and thumb pressure. At this time, the objective of the current work was to demonstrate the

sensor action and characterize the sensor design through simulations; a complete study with different human

subjects along with skin thickness and thumb pressure will be part of a future investigation.

Figure 9-a shows the simulated capacitance for electrode thickness from 1 µm (current study) to

100 µm. The results reveal that a two orders of magnitude increase in the thickness results in only 20-30%

increase in the sensor capacitance. In other words, the capacitance is relatively insensitive to the sensor

thickness, allowing a set of electrodes with high thickness variability (see AFM images in Figs. 5-b, c, d)

to produce a low variation in the sensor capacitance (error bars for untouched capacitance in Fig. 8-a). This

result can be well understood from the EM field line patterns (Fig. 7). The capacitive coupling occurs over

two millimeters in air and in glass which is at a length scale much larger than the electrode thickness of <

2 µm. This result also has two important consequences from manufacturing perspective. First, since the

direct-write printing processes require several passes to build up the electrode thickness, the above result

indicates that a sensor with a very thin electrode built by a single pass printing will not have a very different

native capacitance and electric field distribution when compared to those built with multiple passes. This

is expected to have significant benefit to manufacturing as the number of passes proportionally increase the

manufacturing time23 and hence the cost31. Secondly, the behavior of touch sensors is expected to be

relatively insensitive to the non-uniformity in the electrode thickness, thus saving the cost of quality

control32 of such sensors.

Figure 9-b shows simulated values of capacitance as a function of electrode width, W, of the touch

sensor, expressed as a % of the pitch of the interdigitated pattern of the sensor (dimension (W+G) in the

inset of Fig. 9-b) for a sensor with 5 mm interdigitated region length. Twenty electrode pairs (a total of 40

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electrodes) were used in the simulation. Further, two values of (W+G) are considered, namely, 225 µm and

100 µm. In both the cases, the sensor capacitance increases with an increase in W for a given electrode

pitch (W+G). However, the increase in capacitance is not uniform and divided into three separate regions.

In region 1, the sensor native capacitance increases rapidly for W values from zero to about 2.5%. The

capacitance then increases at a slower rate in region 2 until W is about 90% of the pitch (W+G). In region

3, as W approaches the pitch (W+G), i.e. when the gap between the electrodes is small, the capacitance

increases rapidly. Overall, an increase in W by a factor of 49 for a given pitch (W+G) is shown to increase

the simulated capacitance by a factor of 10. This sensor behavior can be understood from the fact that

majority of the capacitive coupling happens through the electric field lines out of the plane of the sensor

rather than in the in-plane gap between the electrodes (Fig. 7-a, b). Several additional features of the Fig.

9-b that are not clearly seen from the graph should be noted. As expected, the predicted sensor capacitance

is zero when W reduces to zero. On the other hand, as W approaches the pitch (W+G), the gap between the

electrodes approaches zero and the sensor capacitance increases to very high values and is expected to

approach asymptotically to infinity. At W equal to the pitch (W+G), however, the sensor shorts and the

capacitance will be zero. Figure 9-b also shows that the native capacitance of the touch sensor is dictated

by the W as a % of (W+G) more than the actual value of W, an observation highly useful in designing

miniaturized sensor arrays. The results in Fig. 9-b can guide the manufacturing processes as well. For

example, the touch sensor should be designed such that the electrode/gap dimensions should be in region

2, to avoid a small variation in the width of the electrodes (as expected from printing or lithographic

processes) to lead to a high variation in the capacitance of the touch sensor (e.g. as in regions 1 or 3). The

modeling data of the region 2 also shows the quantitative variation in the capacitance change with the

change in the electrode width for a given electrode pitch.

The experimental and modeling results presented in the paper provide a useful framework to design

and additively manufacture capacitive touch sensors with feature length scale down to ~50 µm. The touch

sensor can be printed anywhere, including over a curved, angled surfaces (see Rahman22) such as a Si chip

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or an electronic package, making an integration of on-chip capacitor at arbitrary locations a possibility. The

results also indicate that a single layer of the sensor electrode can suffice to give adequate sensor action at

the frequencies considered in the current work and typically required for IoT applications. It is also

important to consider the limitations of the current study. First, the additive method involves serial writing

and hence can only be scaled up to high volumes by adding the number of print-heads working in-tandem

for printing over a large area. Indeed, such efforts are taking place in the industry with 4-printheads being

used in production for Aerosol Jet technology. In case of inkjet printing, the number of print heads per

equipment is very large, however, the manufacturing accuracy and resolution is not as good as Aerosol Jet

technology21,33. Secondly, the proposed fabrication technique, although suitable for low frequency

applications, can result in considerable resistive losses due to skin-effect at high frequencies. This problem

can be circumvented by printing multiple layers that reduces the surface roughness22, but results in an

increase in the time required for printing and also increases material consumption. The simulations

presented in this work do not account for surface undulations, while, in reality, the surface roughness can

vary randomly between each electrode. This limitation is mitigated by the fact that the sensor capacitance

shows low sensitivity to the electrode thickness variation as well as the total thickness. Future work will

account for advanced modeling of solder interconnects in a 3D layout which will help to improve

predictions of metal resistivity. In addition to customized models, an online library needs to be created to

allow the use of these models for rapid prototyping of larger sensor arrays for applications such as structural

health monitoring; an idea similar to the current practice of foundry development kits available in

conventional CMOS processes. The current work thus demonstrates an environmentally friendly additive

fabrication method for touch sensors and develops a model that can predict the sensor behavior as a function

of variables such as the interdigitated geometry and the surrounding medium. The results from this work

can be used for design, low-cost manufacture, and integration of such sensors into electronic devices.

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7. Conclusions

In this paper, we present the design, an additive manufacturing method, and electromagnetic simulations of

an interdigitated capacitive touch sensor. The study revealed several important aspects of the touch sensor

behavior as below:

a) The Aerosol Jet micro-additive printing allowed the fabrication of sensors with an electrode dimension

down to about 45 µm and a native capacitance of a 1-5 pF. Characterization of the printed sensor using

SEM and AFM studies showed that the sensor electrodes have high thickness variation and a rough surface,

but a low sensor native capacitance variation within 8%. The sensor capacitance increased with the

interdigitated region length.

b) A 3-D electromagnetic model was developed to simulate the touch sensors and find the electric field

distribution for the geometries studied in the paper. The simulations showed a reasonable agreement with

the experimental values for the native capacitance of the sensor (within 12.5%).

c) The simulations also revealed the physical range of the sensor action out of the plane of the electrodes

to be about a millimeter for the geometries used in the current study indicating that this device can also be

used as a proximity sensor under certain conditions.

d) The simulations further showed that the sensor capacitance was relatively insensitive to the thickness of

the sensor electrodes. This explained the experimental observation of a low capacitance variation in spite

of the high variation in the sensor electrode thickness. Lastly, the simulations revealed that the width, W,

of the electrode as a fraction of the electrode pitch (W+G)) is one of the key variables determining the

sensor capacitance and that this dependence is divided into three separate regions. In the first region, the

sensor capacitance increases rapidly until W is about 2.5% of the pitch (W+G). The capacitance then

increases at a slower rate until W is about 90% of the pitch (W+G). As W approaches the pitch (W+G), i.e.

when the gap between the electrodes is small, the capacitance increases rapidly again.

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ACKNOWLEDGEMENTS

We acknowledge the help from Mr. Abhishek Gannarapu, Dr. Arda Gozen, Mr. John Yates and Mr. Scott

Hansen at WSU. We also thank the anonymous reviewers for their valuable comments for substantially

improving the manuscript.

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19

List of Figures

Figure 1: Operating principle of a capacitive touch sensor. a) Schematic 3D view of the sensor, b)

schematic of the working principle of untouched sensor, c) equivalent circuit of the untouched sensor, d)

schematic of the working principle of touched sensor. Here, ε0 is the permittivity of free space (8.85 × 10 -

12 F/m), εr is the relative permittivity of human skin (~40), and ε is the effective permittivity; and e)

equivalent circuit of the touched sensor.

Figure 2: Schematic of an Aerosol Jet System along with of the fabrication process of capacitive sensor

Figure 3: Agilent LCR meter test setup

Figure 4: Optical images of the printed capacitive touch sensor with (a) electrode length of 5 mm, (b)

electrode length of 1.5 mm, and (c) high magnification image of the sensor in (b)

Figure 5: (a) Representative SEM images of sensor electrodes under different magnifications showing a

texture created by sintered nanoparticles. (b) Representative AFM scans of a single electrode at three

different locations, (c) AFM scan of an electrodes from the same device as (a), and (d) AFM scan of an

electrode from a different device.

Figure 6: Simulated electric field of the capacitive sensor (a) Top electric field in dB (reference electric

field, 𝐸𝐸, 630175 V/m), (b) Planar electric field in dB (reference electric field, 𝐸𝐸, 46878 V/m).

Figure 7: (a) Equivalent electrical schematic for the measurement of RC time constant. (b, c, d) RC time

constant plots for sensors with an interdigitated region length of 1.5 mm, 3 mm, and 5 mm, respectively.

The 𝑥𝑥-axis is plotted for one time period. The ring up and ring down time constants are given in Table S2.

Figure 8: (a) Experimental and simulated values for the variation of capacitance with interdigitated

region length for touched as well as untouched state. (b) Experimental and simulated values of the effect

of number of electrodes on the capacitance of a touch sensor with interdigitated region length of 3 mm.

20

Figure 9: (a) Simulated value of capacitance as a function of electrode thickness for three interdigitated

region length values. (b) Simulated value of capacitance as a function of electrode width, W, expressed as

a % of pitch (W+G) for a touch sensor with interdigitated region length of 5 mm. The capacitance

response is divided into three regions indicated on the figure. In region 1, the sensor native capacitance

increases rapidly with W is about 2.5% of the pitch (W+G). The capacitance then increases at a slower

rate in region 2 until W is about 90% of the pitch (W+G). In region 3, as W approaches the pitch (W+G),

i.e. when the gap between the electrodes is small, the capacitance increases rapidly again.

21

Figure 1

Interconnect

a)

c)

d) e)

b)

Touched

Csensor=C0+ Ctouch

ε = ε0εr

Untouched

Csensor=C0

Probing Pad

Interdigitated Electrode Structure

Human Touch

Air

Glass AC

AC

Capacitive Sensor

Capacitive Sensor

22

Figure 2

Substrate

Deposition Head

Printed Electrodes

Substrate Atomizer

X-Y Motion Stage

Standoff

Stream of nanoparticle ink droplets

Printed Electrode

Nozzle

23

Figure 3:

The E4980A LCR Meter

The 16047A Test Fixture

Custom Probing Wires

24

Figure 4:

(a) (b) Interdigitated Region

Length: 5 mm Interdigitated Region

Length: 1.5 mm

Interconnect

Capacitor

(c)

90 µm

132 µm

96 µm

44 µm

Printed Electrode

Bulb

25

Figure 5:

40 µm Electrode

10 µm

500 µm

Electrode

(a)

(b)

(c) (d)

Electrode 3, Sensor 2

Electrode 2, Sensor 1

Electrode 1, Location 1,

Sensor 1

Electrode 1, Location 2,

Sensor 1

Electrode 1, Location 3,

Sensor 1

26

Figure 6:

1 mm

(a)

(b)

1 mm

-70 -60 -50 -40 -30 -20 -10 0

-70 -60 -50 -40 -30 -20 -10 0

27

Figure 7:

(a)

(b)

(c)

28

Figure 7:

(d)

29

Figure 8

(a)

(b)

30

Figure 9

(a)

(b)

Region 1

Region 3 G

W

Electrode Thickness (µm)

Cap

acita

nce

(pF)

31

SUPPORTING INFORMATION

Microscale Additive Manufacturing and Modeling of Interdigitated Capacitive Touch Sensors

Md Taibur Rahman1, Arya Rahimi2, Subhanshu Gupta2*, Rahul Panat1*

1 School of Mechanical and Materials Engineering, 2 School of Electrical Engineering and Computer

Science, Washington State University, Pullman, Washington 99164, USA

*Author to whom correspondence should be addressed; Email: rahul.panat@wsu.edu, sgupta@eecs.wsu.edu

32

S-1: Modeling and Simulation of Sensor in Un-Touched State

Figure S2 shows the substrate model used for the printed capacitor sensors with the interdigitated

region length of 5 mm in Momentum ADS®. A 1 mm thick glass substrate was used with a 1 µm thick

Metal1 (M1) (Ag nanoparticles) extending vertically on top of the glass substrate. Air was used as the

surrounding dielectric medium for initial simulations (Fig. S2-a) with more complex media used to model

touch sensitivity (Fig. S2-b). Table S1 lists various parameters for the substrate model such as metal

resistivity, thickness and dielectric permittivity. Figure S2-c depicts the top-down layout views of the

capacitor including interconnect and pad structures along with dimensions used for modeling. Long

interconnect lengths were used to isolate any pad parasitic capacitances from the sensor. The sensor pads

were simulated with 1 µm thickness in contrast to the fabricated thickness of 4 µm to avoid maintaining

two separate layouts with different metal thicknesses. Simulations with 4 µm thickness for the entire

structure showed only a marginal increase (<0.05%) in capacitance at < 1 MHz thereby allowing the sensor

pads to be simulated with 1 µm thickness without any significant effect. The current layout did not include

3D electromagnetic (EM) components which were added later for the EMPro simulation. A Hammerstead

surface roughness parameter in Momentum ADS® modeled the surface undulations on the metal electrodes

observed from the AFM images, and showed a negligible effect on capacitance and quality factor below

100 MHz. The EM mesh in Momentum ADS® was configured with the “edge mesh” option enabled, a

density of 200 cells/wavelength, and a mesh frequency set to 1 GHz. An image of the EM mesh for the

sensor is shown in Fig. S3. While simulating the touch sensor, the capacitor ports were set such that

Momentum ADS® removes any fringe capacitance at the edge of the metal thus avoiding that the parasitics

being counted twice. Capacitance was then derived from the simulated S-parameters using the following

custom Momentum ADS® equations1:

𝑍𝑍 = stoz (𝑠𝑠, 50)

(1)

33

𝑍𝑍𝑖𝑖𝑖𝑖 = 𝑍𝑍(1,1) − 𝑍𝑍(1,2)𝑍𝑍(2,1)

𝑍𝑍(2,2)

(2)

C = imag 12𝜋𝜋𝜋𝜋𝑍𝑍𝑖𝑖𝑖𝑖

,

(3)

where “stoz” is a custom function to convert S-parameter data to z-parameter data, and “imag” returns the

imaginary part of a complex number.

S-2: Modeling and Simulation of Sensor in Touched State

The touch sensitivity of the capacitive sensors was further simulated through a model developed

for human touch in Momentum ADS® (Fig. S2-b). A 2 µm layer of air was left above M1 to simulate a

possible gap caused by the plastic layer covering the 0.5 – 2 micron high sensor electrodes above the

substrate. A 100 µm thick plastic film above the air gap modeled the insulator between the thumb and the

sensor. This insulator was used as a buffer between the human thumb and the sensor to avoid shorting the

structure and contaminating the electronics. The thumb dielectric consisted of multiple layers of different

dielectric properties. At the frequencies of interest, all the tissues were expected to affect the dielectric,

including those for hypodermis, dermis, and epidermis. However, the thickness of these layers varies

considerably (e.g. hypodermis from 0.3-3 mm, dermis 0.3-3 mm, and epidermis 0.5-1.5 mm)2, resulting in

considerable difference in the effective dielectric from person-to-person and even for the same person

contacting the sensor at different times (due to factors such as difference in the applied pressure). Here, we

modeled the dry human thumb as a single dielectric medium with relative permittivity, εr=402. The final

layer was modeled as M2 which grounded the human thumb. The layout with metal layers and interlayer

dielectric materials was same as that shown in Fig. S2-c. A 3-port S-parameter simulation was carried out

to characterize the dry thumb test case.

34

S-3: 3D E-Field Simulation in ADS EMPro

A 3D electric field (E-field) estimation was done through EMPro® for the model imported from

Momentum ADS®. Figures S4-a, b, and c show the capacitor structure in EMPro®. Boundary boxes are

placed at the edge of the structure to define 3D simulation space. The Finite Element Method (FEM) solver

option was used in EMPro® to achieve faster convergence. The E-field was estimated both in-plane and

out-of-plane directions as shown in Figs. 6-a, b, respectively, using EMPro® near-field planar surface sensor

features.

S-4: Internal Circuit Schematic

Figure S6 shows the internal circuit schematics of the LCR meter referenced from Agilent27 when

a Device Under Test (DUT), the capacitive touch sensor in this case, is connected to the terminals. An

active-feedback circuit called as “Auto-Balancing Bridge (ABB)” (Fig. S6) is used to model one end of the

DUT as a virtual ground and calibrate the current during the initial calibration steps accounting for any

series resistance (solder or lead resistance). As the capacitor sensor is brought in vicinity to external

parasitics (human thumb for example), the ABB tries to auto-adjust the current through the virtual ground

by changing the amplifier gain to maintain the node Lp at virtual ground. The negative feedback causes the

circulating AC current to reduce resulting in a ‘false’ decrease in measured capacitance rather than an

increase as expected. Thus, once calibrated, the LCR meter can’t be used to measure a touch sensitivity on

the fly. This observation was further verified in the lab on the LCR meter. To overcome this issue, the

capacitance is measured directly using the RC time constant observed on an oscilloscope, with the measured

results shown in Figs. 7-b, c, d.

35

REFERENCES

1 Agilent. Advanced Design System documentation for Momentum. . http://cp.literature.agilent.com/litweb/pdf/ads2008/mom/ads2008/index.html (2008).

2 Nanzer, J. A. Microwave and millimeter-wave remote sensing for security applications. (Artech House, 2012).

36

Supporting Information

Table S1: Electrical properties of the touch sensor used for the electromagnetic simulations

Parameter Value Substrate Permittivity 3.9 Plastic Permittivity 3.7 Dry Thumb Permittivity 40 Substrate Thickness 1000 µm Metal 1 and Metal 2 Thickness 1 µm Air Gap Between Plastic and Metal 1 2 µm Plastic Thickness 100 µm Dry Skin Thickness 1000 µm Metal 1 and Metal 2 Resistivity 3.23 µ Ω.cm

37

Table S2: Rise time constant and fall time constant for the plots in Fig. 7

Interdigitated Region Length

(mm)

τrise_touched τrise_untouched τfall_touched τfall_untouched

(µs) (µs) (µs) (µs)

1.5 0.426 0.233 0.355 0.214 3 0.454 0.254 0.436 0.245 5 0.603 0.337 0.541 0.318

Table S3: Data used to plot Fig. 8

Interdigitated Region Length, (mm)

Number of

Electrode Pairs

State Capacitance

from Simulations,

(pF)

Capacitance from

experiments (Mean) (pF)

Capacitance from

experiments, (Std Dev)

(pF)

Experimental Method

1.5 20 Untouched 1.98 1.97 0.18 LCR Meter

1.5 20 Touched 3.99 3.91 0.23 Oscilloscope*

3 20 Untouched 3.05 3.28 0.13 LCR Meter

3 20 Touched 5.86 7.87 1.38 Oscilloscope*

5 20 Untouched 4.52 5.4 0.13 LCR Meter

5 20 Touched 8.38 10.66 1.18 Oscilloscope*

3 8 Untouched 1.66 1.33 - LCR Meter

3 14 Untouched 2.36 - - -

* The RC time constants for the touched and untouched states were directly measured using an oscilloscope to obtain the ratio of the capacitance in the touched state to that in the untouched state (see section 5). This ratio along with the untouched capacitance from the LCR meter gave the experimental value of the capacitance in the touched state.

38

List of Supporting Figures

Figure S1: Image of the Aerosol Jet micro-additive manufacturing machine used to fabricate the sensors in the current study.

Figure S2: Sensor modeling using Momentum ADS® showing a) model to simulate the sensor in untouched state, b) model to simulate a dry human thumb touching the sensor, c) top layout view of the sensor with dimensions used for the simulations in the untouched and untouched cases.

Figure S3. Electromagnetic (EM) mesh generated by the software for sensor structure with ~200 cells/wavelength at a mesh frequency set to 1GHz in Momentum ADS®.

Figure S4: Simulation of the electric fields of the capacitive sensor. a) EMPro imported structure. b) EMPro perpendicular planar sensor. c) EMPro planar sensor 'Cutting' into the structure in the x direction.

Figure S5: Set-up to measure interdigitated touch sensor capacitance.

Figure S6: Internal circuit schematics of the LCR meter when a Device Under Test (DUT), i.e., the capacitive touch sensor, is connected to the terminals.

39

Figure S1

UV Laser

Print-head with nozzle

Aerosol from ultrasonic atomizer

UV controls

Platen

40

Figure S2

89 µm

132 µm

96 µ

m

45 µ

m

(b)

(a)

(c)

41

Figure S3:

42

Figure S4:

Measuring Port

Perpendicular Planar Sensor

Planar Sensor ‘Cutting’ into the structure in the x

direction

(a)

(b) (c)

43

Figure S5:

Active Probe

Function Generator

The RC Circuit

Common Ground

Oscilloscope

44

Figure S6: